What is Wrong?

Wrong Theory

Neoclassical growth theory, as developed by Robert Solow (1956, 1970) and his followers, has dominated recent economic thinking about long-term growth. The basic mathematical framework used in neoclassical analysis is the Cobb-Douglas production function

1. Y = A e^mt K^a L^{(1 - a)}

Where

Y is output, or GDP

A is the productivity, or efficiency of production, due to technological progress at a point in history t = 0

m is the rate of productivity growth due to technological progress

t is time

K is the stock of physical and human capital

L is the stock of unskilled labor

a is the percent change in output from each percent change in capital (a is empirically observed to be about .3)

1-a is the percent change in output from each percent change in labor

Production is a process that acts on the inputs of labor, capital, and raw materials to produce output of goods and services. Productivity determines how much output can be produced for any given amount of input. Productivity depends on the level of the technology used in the production process. Technology is knowledge of how to do things. Technology is manifested in the skills of the labor force, the techniques of management, the quality of the infrastructure that supports production, and the design of manufacturing equipment and software used in the production process. The current level of technology is the sum total (or integral) of technical knowledge accumulated over all past history (up to t=0). The current level of productivity depends on the current level of technology.

If we differentiate formula (1) and divide by output, we get the % rate of economic growth

2. dY/Y = m + a dK/K + (1-a) dL/L

Where

dY/Y = % rate of economic growth

m = rate of productivity growth

dK/K = % rate of capital formation

dL/L = % rate of growth of the labor force

Equation (2) suggest that there are two fundamental types of economic growth. One is input growth (i.e., increases in capital dK, and labor dL). The other is productivity growth m.

Input Growth

Input growth generates economic growth by adding more workers to the labor force, increasing the stock of capital equipment, and using more raw materials. Input growth is fundamentally limited by the number of trained workers, the amount of available equipment, and the ability of the environment to support demands for raw materials.

Productivity Growth

Productivity growth generates economic growth by improving the efficiency of plant and equipment, by increasing the skills of labor and management, and by developing better materials and more efficient methods for acquiring resources.

Economic growth based on productivity growth does not require more workers, capital, or raw materials -- simply better. Productivity growth can allow the same number of workers to produce more output, and earn correspondingly higher wages. Productivity growth can reduce the amount of capital equipment required for production. This allows businesses to purchase more and better machines at lower cost, and hence to earn higher profits. Productivity growth also usually results in lower prices and higher quality for consumers.

Productivity growth can enable more goods and services to be produced with fewer resources and less waste. If productivity growth is rapid enough, economic growth can occur while input actually falls. Economic growth based on productivity growth can thus actually reduce demands for resources and improve the quality of the environment.

Limits to Growth

Perhaps the most important distinction between input growth and productivity growth is in regard to the limits to growth. Environmentalists argue that economic growth is limited by constraints imposed by the finite resources of the planet Earth. Depletion of resources, increasing levels of pollution, and the inability of the environment to support exponentially rising demands for resources are therefore seen as preventing rapid sustainable economic growth. They fear that attempting to provide a rising standard of living for a growing population will bring environmental catastrophe. This viewpoint is reflected in the "Limits to Growth" models financed by the Club of Rome. These computer models predict world wide environmental collapse unless drastic measures are taken to reduce economic growth. (Meadows 1972)

However, most such environmentalist arguments apply only to the part of economic growth that comes from input growth. For example, the Meadows computer models neglect productivity growth and the effect of investment on technological knowledge. They make no provision for the ability of market prices to force substitutions for scarce resources, and fail to take into account the ability of technology to create new resources, or to restore damage done to the environment.

Without question, economic growth produced by input growth is subject to many limits. But economic growth produced by productivity growth has no limits, because productivity growth itself has no fundamental limits. Productivity is not physical and is not subject to physical limits. Productivity is the efficiency of production. It depends entirely on technology. Productivity growth results from improvements in technology. Improvements in technology result from research and development, installation of modernized equipment, and education and training of labor and management.

Unlike physical resources, technology is not finite. Technology is simply knowledge, and knowledge is an inexhaustible resource. New knowledge makes it possible to substitute new materials for old, and create resources from what was not previously considered useful. Unlike other economic factors, technology is not subject to depreciation or diminishing returns. Knowledge does not wear out or get used up, but instead increases exponentially with use. The use of knowledge produces more knowledge. The more that is known, the easier it is to discover new things, and there is no limit to what there is to know.

The only real limit to knowledge is the amount of money, time, and effort invested in pursuit of it. The only limit to productivity growth is the amount of wealth that society is willing to invest in education, research, development, and implementation of more efficient production process technology.

This implies that the only real limit to economic growth is the rate of investment.

Endogenous Growth Theory

The neoclassical theory of growth is seriously flawed in that it fails to recognize the impact of investment on productivity growth. Instead, it asserts that productivity growth is an exogenous variable that occurs "naturally" as a simple function of time, unaffected by factors (such as investment) that are subject to economic policy.

To the layman, this seems absurd on its face. Solow himself admits this gives us "a theory of growth that leaves the main factor in economic growth unexplained" (Solow 1994). There is a growing body of evidence and opinion (Romer, 1990, 1994; Grossman and Helpman, 1994; Caballero and Jaffe 1993) that productivity growth is instead an endogenous variable -- not simply a function of time. There are many good reasons to believe that productivity growth rate is, in fact, a direct causal function of the investment rate. Technological knowledge, and hence productivity growth is almost certainly effected by the amount of money and effort invested in research and development, as well as by the rate of procurement of modernized equipment, and the level of education and training of labor and management.

A report published by the Competitiveness Policy Council Report (1993), a prestigious bipartisan federal advisory committee appointed by the President, House, and Senate of the United States, suggests not only that productivity growth can be effected by the investment rate, but cites economic models that predict how much. The C.P.C. report suggests that the productivity growth rate could be doubled (from less than 1 percent to at least 2 percent annually) by increasing the nation’s investment rate by at least 4 to 6 percent of GDP, or about $300 billion per year at current prices.

There is a great body of empirical evidence (Friedman 1989, Dunn 1980) demonstrating a positive correlation between the investment rate and the productivity growth rate. One set of data is plotted in Figure 1.

This data shows that, over more than two decades between 1960 and 1983, the U.S. invested about 17% of GDP, and achieved about 1.5% productivity growth. Over the same time interval, European countries invested, on average, about 24% of GDP and experienced an average productivity growth rate of around 3.6%. Japan (and several other nations on the Pacific rim such as Taiwan, South Korea, Singapore, and Hong Kong) invested around 32% of GDP and achieved productivity growth rates around 6%.

Regression of the data in Figure 1 onto a straight line produces the formula

3. mL = .3 (I - D)

Where

mL is the labor productivity growth rate

I is the investment rate as a percent of GDP

D is depreciation as a percent of GDP (around 12%)

In words, formula (3) states that the rate of productivity growth can be expressed as a function of the rate of investment. It suggests that a nation must invest about 12 percent of GDP in order to prevent productivity from declining because of plants and equipment wearing out, skilled workers growing old and dying, and depletion of resources. For every three percent of GDP invested over and above 12 percent, the productivity growth rate will rise about one percent.

The clear implication is that productivity growth is an endogenous variable that is strongly effected by the rate of investment. Neoclassical growth theory is therefore seriously flawed in that it fails to appreciate the powerful effect of investment on the productivity growth rate.

We can attempt to remedy this flaw if we take the value of productivity growth rate from formula (3) and substitute it in formula (2). Before we can do that however, we must take into account the difference between total factor productivity growth rate m and labor productivity growth rate mL. Labor productivity can be expressed as

4. Y/L = A e^mt K^a L^-a

Differentiating and dividing by labor productivity gives labor productivity growth rate

5. mL = m + a (dK/L)/(K/L) = m + a (dK/K - dL/L)

or

6. m = mL - a(dK/K) + a(dL/L)

Substituting (6) in (2) gives

7. dY/Y = mL + dL/L

In words, the rate of economic growth is the labor productivity growth rate plus the labor growth rate. Substituting (3) in (7) along with the current growth in labor dL/L = 0.011 gives

8. dY/Y = 0.3 (I - 0.12) + 0.011

Formula (8) shows that for the current U.S. economy, the economic growth rate is strongly dependent on the investment rate. It suggests that for the economy as a whole, the marginal rate of return on investment is 30%. In other words, for every dollar invested above the depreciation rate, thirty cents is returned in economic growth the first year, and every year thereafter. This is a phenomenal rate of return. However, this is the rate of return to society as a whole -- not what is realized by the individual investor. The private investor receives only the return paid to the increment in capital, or

9. 0.3 (dK/K) = 0.12 (I - D)

assuming K = 2.5 Y

This is a marginal rate of 12%. The private investor does not capture all of the benefits from productivity growth over the whole economy. As a result, market forces can never produce as much investment as is socially desirable.

This conclusion is supported by the results of Mansfield (1972, 1977) who showed that the social return on investment generally exceeds the benefits realized by private investors by at least a factor of two. This analysis strongly suggests that any economic system that relies solely on private market incentives for investment will chronically invest substantially less than what is optimal from the point of view of the society as a whole.

Investment

Investment is the commitment of capital and resources to productive activities that are expected to increase output by enough to pay back the investment and generate future profits.

Investment in research produces new technological knowledge, new inventions, and new materials. Investment in development produces more efficient machines, improved process technology, and more competitive industries. Investment in education and training leads to improved management techniques, better worker skills, a more productive work force. Investment in modernized plant and equipment speeds the commercialization of new knowledge, creates more efficient methods of production, fosters the use of new and improved materials, and speeds the development of more efficient methods for extracting or recycling conventional materials. The rate of investment determines the rate of technological advance, and hence the rate of productivity growth.

Of course, investment involves risk, and investments take time to pay back and return a profit. Not all investments pay back quickly, and some don’t pay back ever. There are many case histories of unwise investments that failed. Many private fortunes have been lost, and many government projects have failed to return a net gain to the tax payer "investors". Innumerable "pork-barrel" projects have resulted in benefits to narrow political constituencies at a cost to the general public that is never recovered.

Nevertheless, risk can be reduced by diversification, and unwise investment decisions can be minimized by honest competitive selection of investment proposals. There exist ways to select promising lines of research, talented researchers, skillful managers, and good business plans. Successful investment strategies are known to those skilled in the art, and profitable investing is a highly developed profession.

The biggest investment risks lie in ignoring the rules of wise investment, for example, by investing in ventures that are ill conceived, highly speculative, fraudulent, or designed so as to increase consumption more than production. To be consistently successful, investment decisions must be made by smart well-trained people that are both skilled in the art of investing, and motivated primarily by an interest in seeing their investments pay substantial dividends.

When investments are wisely made, in sufficient amounts, with adequate diversification, the result is technological progress, productivity growth, and economic growth. For entire nations, a high rate of investment can produce the productivity growth necessary to sustain a rapid rate of per capita economic growth.

Unfortunately, most nations, including the United States, invest at a rate that is far below what is optimal from the standpoint of social benefit. For example, the optimal (or Golden Rule) rate of investment is the point where the marginal return on investment is equal to the depreciation rate (Phelps 1961). In the U.S., the marginal return on investment is roughly 12% per year. The depreciation rate (as a percentage of capital stock) is only about 4%, or three times less. It is therefore clear that the U.S. is investing at a rate that is far below optimal.

The Worldwide Slowdown

There has been a world wide slowdown in both economic growth and productivity growth over the past two decades. Many economists have tried to explain this slowdown in terms of environmental constraints on resources, the rise in oil prices, government environmental regulations, or even that the world is running out of new ideas about how to produce goods and services (Symposium 1988). Many environmentalists have seen in the slowdown a verification of their "limits to growth" theory.

However, the facts are that most raw materials are not in short supply, oil prices are currently near an all time low in real dollars, and there exists a vast store of productivity enhancing technology waiting in the laboratory for the investment capital necessary to transfer it into commercial practice. The decline in productivity growth is much more easily explained by the decline in the investment rate which has taken place over the past two decades. During that period, savings and investment have declined in most industrial countries throughout the world, including Japan, by an amount sufficient to cause the observed drop in productivity and economic growth. In America, the net national saving rate (private savings less government deficits) has dropped from 8.8% of net national product during the 1960s to only 2.0% during 1990-91. (Competitiveness Policy Council 1993) The net U.S. investment rate has dropped somewhat less, only because of foreign investments in the United States. (Gordon 1993)

The clear implication of both theory and empirical evidence is that slow productivity growth and slow economic growth are caused by inadequate investment. A lower rate of investment produces slower productivity growth and eventually slower economic growth. There is good reason to believe that an increase in the investment rate would produce a corresponding increase in the productivity growth rate, as well as in the economic growth rate.

Unfortunately, policies that would raise the investment rate are extremely difficult to implement, and there are many reasons why nations do not generate adequate rates of investment. One of the most common reasons is the conflict between consumption and investment.

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